Hong–Ou–Mandel visibility metrology of stochastic phase-matching noise in spontaneous parametric downconversion crystals

We propose a protocol for probing mechanically induced stochastic phase-matching fluctuations in spontaneous parametric downconversion (SPDC) by Hong–Ou–Mandel (HOM) interferometry. The analysis is formulated for collinear type-II SPDC in β-barium borate (BBO). We distinguish the ideal white-jerk limit from the experimentally relevant finite-bandwidth regime. In the ideal limit, the incremental phase variance generated during a photon transit scales as L5; however, for a 5-mm BBO crystal, the transit time is only about 29 ps, so a piezoelectric mechanical drive is quasi-static on this time scale and the L5 law is not assumed as a direct experimental signature. Instead, the measured acceleration power spectral density and the mechanical transfer function are used to calculate the finite-bandwidth phase fluctuations. The connection to HOM visibility is derived through the biphoton joint spectral amplitude: stochastic phase mismatch modifies the phase-matching function, and the ensemble-averaged spectral-exchange overlap determines the coincidence dip. A frequency-independent common phase cancels from this overlap and therefore does not reduce HOM visibility. The resulting formulation provides a directly testable route for phase-stability metrology without requiring the experimentally inaccessible white-noise approximation.